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Separable Initial-Value Problems worksheets

Solve bounded separable IVPs while preserving equilibrium branches and maximal valid intervals.

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Solve bounded separable IVPs while preserving equilibrium branches and maximal valid intervals.

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Solutions include their mathematical boundaries

Worked keys preserve equilibrium branches, maximal intervals, recurrence rounding, integrating factors, and carrying-capacity interpretations wherever they apply.

Learning objective

What this activity builds

Apply an initial condition without losing divided-out solutions or crossing singularities.

Worked example

What belongs in a complete differential-equation solution?

The governing equation, valid solution steps, initial-condition substitution, and any interval, units, equilibrium, or approximation label.

The worked key keeps the method and interpretation visible instead of presenting only a final expression.

Teaching notes

Make the practice count

  • Check a symbolic solution by substitution into the differential equation.
  • Keep exact formulas separate from Euler approximations.
  • Ask what the result means on the original interval and in the stated units.

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Math SheetNameScoreTeacherDateSeparable Initial-Value ProblemsSeparate variables, retain every equilibrium solution, apply the initial condition, and state the maximal interval containing the initial point.1.Solve y' = 2y, y(2) = -2. Include equilibrium solutions and the maximal interval.2.Solve y' = 1(y-0)^2, y(0) = 1. Include equilibrium solutions and the maximal interval.Show recurrence rows, integrating factors, equilibria, intervals, and units when applicable.math-sheet.comPage 1 of 2
Math SheetNameScoreTeacherDateSeparable Initial-Value ProblemsSeparate variables, retain every equilibrium solution, apply the initial condition, and state the maximal interval containing the initial point.3.Solve y' = -3(y-2)^2, y(2) = 2. Include equilibrium solutions and the maximal interval.4.Solve y' = -2y, y(0) = 0. Include equilibrium solutions and the maximal interval.Show recurrence rows, integrating factors, equilibria, intervals, and units when applicable.math-sheet.comPage 2 of 2

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